A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...

The inversion problem for square matrices having the structure of a block Hankel-like matrix is studied. Examples of such matrices in&de Hankel striped, Hankel layered, and vector Hankel matrices. It is shown that the components that both determine nonsingularity and construct the inverse of such matrices are closely related to certain matrix polynomials. These matrix polynomials are multidimen...

Consider random symmetric Toeplitz matrices Tn = (ai−j) n i,j=1 with matrix entries aj , j = 0, 1, 2, · · · , being independent real random variables such that E[aj ] = 0, E[|aj |] = 1 for j = 0, 1, 2, · · · , (homogeneity of 4-th moments) κ = E[|aj |], and further (uniform boundedness) sup j≥0 E[|aj |] = Ck <∞ for k ≥ 3. Under the assumption of a0 ≡ 0, we prove a central limit theorem for line...

We present forms of the classical Riesz–Kolmogorov theorem for compactness that are applicable in a wide variety settings. In particular, our theorems apply to classify precompact subsets Lebesgue space $$L^2$$ , Paley–Wiener spaces, weighted Bargmann–Fock and scale Besov–Sobolev spaces holomorphic functions includes Bergman general domains as well Hardy Dirichlet space. criteria characterize c...

The mathematical theory of kernel (null space) structure of Hankel and Hankel-like matrices is applied to the problem of blind equalization of co-channel signals. This work builds on recently introduced ideas in blind equalization where the symbols are treated as deterministic parameters and estimated directly without estimating the channel first. The main contribution of the new approach is th...

The Canonical Polyadic tensor decomposition (CPD), also known as Candecomp/Parafac, is very useful in numerous scientific disciplines. Structured CPDs, i.e. with Toeplitz, circulant, or Hankel factor matrices, are often encountered in signal processing applications. As subsequently pointed out, specialized algorithms were recently proposed for estimating the deterministic parameters of structur...

The papers [MRT05], [CGS07], [XXG12], and [XXCBa] have combined the advanced FMM techniques with transformations of matrix structures (traced back to [P90]) in order to devise numerically stable algorithms that approximate the solutions of Toeplitz, Hankel, Toeplitzlike, and Hankel-like linear systems of equations in nearly linear arithmetic time, versus classical cubic time and quadratic time ...

Structured linear algebra techniques enable one to deal at once with various types of matrices, with features such as Toeplitz-, Hankel-, Vandermondeor Cauchy-likeness. Following Kailath, Kung and Morf (1979), the usual way of measuring to what extent a matrix possesses one such structure is through its displacement rank, that is, the rank of its image through a suitable displacement operator. ...

In this thesis we study operators, and spaces of operators on a Hubert space defined by intertwining relations. The classical Hankel operators are those operators which intertwine the unilateral shift and its adjoint. We consider generalised Hankel operators relative to shifts and relative to families of shifts and give generalisations of the classical theorems of Nehari and Hartman. In contras...

A class of functions is speciied which give rise to semibounded quadratic forms on weighted Bergman spaces and thus can be interpreted as symbols of self-adjoint Berezin-Toeplitz operators. A similar class admits a probabilistic expression of the sesqui-analytic integral kernel for the associated semigroups. Both results are the consequence of a relation of Berezin-Toeplitz operators to Schrr o...